First thing you have to understand is the numbers. 0 is head up on the center, 2 is head up on a guard on either side, 4 is head up on a tackle. A 1 tech will line up in the gap between the center and the guard but generally shades towards the TE or the strong side of the formation. A 3 tech lines up between the guard and the tackle on the weak side. There are of course a ton of variations and other ways to do it based on play calls, weaknesses, and things you want to attack but lets stick to the basic concept.
The difference between a 1 tech and a 3 tech is, and again I am talking in generalities, you want your 1 tech to be a big strong fatty in the 320-350 lb range whose soul job is to absorb both a guard and the center blocking them. He needs to keep two guys on the line for 2-3 seconds so that the linebacker behind him is clean and able to make a 1 on 1 tackle on the RB. A 1 tech wont have a ton of stats or even look like they are all that important. They face a ton of combo blocks where the guard helps the center get him 2 yards off the ball and then slids to the LB. Think Wilfork he was absolutely the stereotype 0 tech NT or 1 tech.
Now a 3 tech needs to be a little more versatile as they play both the run and the pass. They tend to be in the 290-300 lb range. Generally they go 1 on 1 with a guard and have to beat him to a spot. You can do that either with power, speed, quickness, lots of different types and ways to do it but they arent usually asked to take on 2 people like a 1 tech. If I was designing a 3 tech it would end up looking alot like Warren Sapp....without the douche.
Here's where it gets fun. In a 3-4 you have 1 really big fatty in the middle who has to protect 2 LBs and (2) 3 tech type players. Think of the pats d line in the early 2000's. They had 3 really big really good fat guys that chewed up blockers and let the Linebackers make plays. In today's 4-3 you hear more of Lawrence Guy cuz he is expected to make some tackles instead of just absorbing blockers.
Now you can 1 gap or 2 gap from any tech in either formation. A 1 tech DT could be lined up towards the strong side but be responsible for the weak side A gap cuz a LB is going to blitz the strong side A gap. 1 gapping versus 2 gapping is more a risk/reward philosophy then a body type. 2 gapping is a reaction based defense that won't make a big play but is less likely to give up a big play either. 1 gapping is more of an attacking defense where the goal is to be 2 yards in the back field in your gap. Yeah you might get more sacks and tackles for a loss, but you open up cut back lanes and escape routes.
Hope that helped with the basics. Like I said before there are a ton of variations but its mostly semantics based on personal. If you have great aggressive players that are better at do this and be there you probably want a 4-3 1 gap defense. If you have smart players that can do alot of everything a 3-4 2 gap works too. The problem with the pats right now is besides Guy (a 3 tech body type) they got a whole lot of nothing at the 1 tech body type when you should have 2. I agree that a proper 1 tech is priority 1 behind QB of the future.